Matilda III, a sweet Ragdoll adopted from the North Shore Animal League this summer, replaced her 15-year-old predecessor, Matilda II, who retired to a staff member’s home.

Cats have been a fixture at the Algonquin Hotel for almost 80 years. Rusty, later named Hamlet, strayed into the building in 1932; since then, 10 different cats have graced the laps of America’s greatest authors and welcomed famous guests to the classy comfort of the hotel’s lobby lounge.

But alas, the health department, pressured by New York City Mayor Michael Bloomberg, has taken on a campaign of slapping major fines on minor violators probably while leaving rat-infested salmonella factories to keep on serving their plague-ridden food.

New York City health code forbids live animals from being in food service establishments unless those animals happen to be service dogs. That’s perfectly understandable — nobody wants to think a cat’s litterbox paws were traipsing across tables and kitchen counters. But Algonquin managers say they have an electronic fence to keep her away from food-service and food prep areas.

A bad grade in a health inspection can ruin a restaurant, so the staff was justifiably concerned when the DOH pointedly “reminded” them of the regulation. But oddly enough, the hotel was given a preliminary inspection on Nov. 10 and received 20 violations, worth a B grade unless they’re corrected none of which involved Matilda.

Now the cat is confined behind the Algonquin’s front desk to temporarily appease the Health Police. I braved the fetid cesspool of the Post’s comment section and found that amidst all the predictable political flaming and snide comments, Matilda’s supporters are up in arms at her unjustified banishment. One wrote, “Keep your head held high like the queen you are, Matilda. You are magnificent!”

And she’s doing just that. With cat class and cat style, “She’s in the lobby smiling and posing. She’s at the front desk,” said hotel spokeswoman Alice Dealmeida.

If you want to see how much people love Matilda — and lend your support — without wading through gallons of electronic sewage, I recommend you visitMatilda’s Facebook page instead of the Post.

Doesn’t the health department have anything better to do than get all over the case of one well cared-for, well-loved, and well-trained cat, who has never done any harm to anyone? Cats have lived at the Algonquin for generations, and nobody’s gotten sick from feline-borne pathogens.

I know people who have gone to (and stayed at) the Algonquin precisely because Matilda is there to greet them. If I were in New York and I had the money to get a room in a high-class hotel, I’d stay at the Algonquin in a heartbeat. Matilda would be a great “cat fix” for this lonely, catless traveler.

If she stays in the lobby and out of the food prep areas, what’s the problem? Leave Matilda alone and let her do what she does best!